Anthony has 2 containers. Container R and Container S are of different capacities. If Container R is filled by a tap at a rate of 5 litres per minute and Container S is filled by a tap at a rate of 6 litres per minute, when Container R is completely filled, 7 litres of water flowed out from Container S. If Container R is filled by a tap at a rate of 4 litres per minute and Container S is filled by a tap at a rate of 2 litres per minute, when Container R is completely filled, Container S is only half-filled. What is the capacity of Container S? Express your answer in litres.

	Scenario 1		Scenario 2
Container type	Container R	Container S	Container R	Container S
Volume of the container	5 u	6 u - 7	4 p	2 p x 2 = 4 p

Let 1 u be the time taken for Scenario 1.
Let 1 p be the time taken for Scenario 2.

5 u = 4 p --- (1)
6 u - 7 = 4 p
6 u = 4 p + 7 --- (2)

Make u the same.

(1) x 6
30 u = 24 p --- (3)

(2) x 5
30 u = 20 p + 35 --- (4)

(3) = (4)
24 p = 20 p + 35
24 p - 20 p = 35
4 p = 35
1 p = 35 ÷ 4 = 8.75

Volume of Container S
= 4 p
= 4 x 8.75
= 35 ℓ

Answer(s): 35 ℓ